Precision Thermodynamics of the Fermi polaron at strong coupling

TL;DR

This paper presents the first controlled thermodynamic calculations of the Fermi polaron at strong coupling using AFMC methods, providing new insights into its properties and comparison with experiments.

Contribution

It introduces a finite-temperature AFMC approach to study the Fermi polaron at strong coupling, overcoming previous computational challenges.

Findings

Calculated the contact as a function of temperature and coupling strength.

Found good agreement with variational approaches at unitarity.

Compared results with experiments, noting discrepancies away from unitarity.

Abstract

The Fermi polaron problem, which describes a mobile impurity that interacts with a spin-polarized Fermi sea, is a paradigmatic system in quantum many-body physics and has been challenging to address quantitatively in its strong coupling regime. We present the first controlled thermodynamic calculations for the Fermi polaron at strong coupling using finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods in the framework of the canonical ensemble. Modeled as a spin-imbalanced system, the Fermi polaron has a Monte Carlo sign problem, but we show that it is moderate over a wide range of temperatures and coupling strengths beyond the unitary limit of the BCS-BEC crossover. We calculate the contact, a quantity which measures the strength of the short-range correlations, as a function of temperature at unitarity and as a function of the coupling strength at fixed temperature and find good agreement with a variational approach based on one particle-hole excitation of the Fermi sea. We compare our results for the contact with recent experiments and find good agreement at unitarity (within error bars) but discrepancies away from unitarity on the BEC side of the crossover. We also calculate the thermal energy gap at unitarity as a function of temperature.